I never really print bigger than 17 inches wide, but I'm looking for a printer that is efficient with regards to ink consumption. Is something like the Epson 7890 more efficient than say an epson 3880?
No, they will use about the same amount of ink. The ink costs are less for the larger printer, because the cartridges are larger so you pay less per milliliter. You are essentially buy ink in bulk. Instead of 80 ml, you are buying 150, 350, or 700 ml cartridges.
Also what is the difference between the epson 7890 and the epson 7900?
Orange and green inks. Slightly larger gamut, unless you are using a RIP that can better utilize the two extra inks, then you can get greater print longevity. The yellow ink fades faster than the others, so using O or G instead of Y to make a color, when that is possible, helps with fading.
Brian A